Results 22 - MIXTURE CODING AND ODOR-SEGMENTING KENYON

2. MIXTURE CODING AND ODOR-SEGMENTING KENYON

2.1 Results 22

2.1.1 Representations of binary mixtures by PNs

Because odor representations by PNs are highly distributed and varied in time (Fig. S2.3), because their activity patterns are decoded by individual KCs on which converge many PNs (59) and because KCs have very short effective temporal integration windows (53, 60), it is appropriate and more informative to examine PN responses as time-series of instantaneous population vectors, or trajectories, in an appropriately reduced state space (7, 58, 71, 79). Figure 2.1 illustrates these PN population trajectories for a set of representative stimuli. Figures 2.1A-C concern binary mixtures: we plot the evolution of the representation for the odors citral, octanol, and their 1:1 mixture. The mixture trajectory lies somewhere in between those for the two components, suggesting a simple linear combination. This was confirmed by correlation analysis performed in full PN space. This relatively simple combination was not entirely predictable from the responses of single PNs to binary mixtures, for those often deviated significantly from the arithmetic sum of the responses to the components (Fig. S2.3; compare open and filled PSTHs).

This suggests that significant correlations exist between the responses of different PNs to the same stimulus, and that those linearize the population's combined output, at least for binary mixtures. Figure 2.1B represents concentration series for these three stimuli (the two pure

odors and their binary mixture). Extending previous results (7), we find that concentration series for 1:1 mixtures, as for single odors, generate families of closely related trajectories (lower-dimensional manifolds), clustered by odor rather than concentration. In a final experiment, we

“morphed” one odor into the other in 11 intermediate steps (Fig 2.1C).

Contrary to recent results in the zebrafish olfactory bulb (Friedrich et al., in press), we observed no sudden transition but rather, a gradual shift of the population trajectory corresponding to one odor to that for the other odor, via their 1:1 mixture trajectory. Thus the encoding space defined by PNs appears to optimize the spread of odor representations to accommodate even small changes in the stimulus. While the responses of single PNs often deviate from the linear combination of the responses to their components, the population output is reasonably well approximated by linear summation.

Figure 2.1 Representations of single odors and their mixtures are spread orderly in PN coding space.

A-C. Trajectories representing PN-ensemble responses to binary mixtures. PN activity is represented as a point in 168-D space, where each dimension represents the firing rate of one of the 168 PNs during one 50-ms time bin. Data analyzed using LLE and projected in the space of the first three LLE components (see Methods). Arrows indicate direction of motion. Three seconds are represented, beginning at odor onset; odor pulses are 300 ms long; each trajectory composed of a sequence of 50ms-bin measurements, averaged over three trials. (A) PN Population responses to single odors (citral: green; octanol: red) and to their 1:1 mixture (yellow). Initially at a resting state (origin: O), the PN population responds with stimulus-specific trajectories. (B)

Trajectories to different concentration series of citral, octanol (30, 60, 80, 100, 120, 140 ml/min) and their 1:1 mixture (30:30, 60:60, 80:80, 100:100, 140:140 ml/min).

Similar to trajectories for pure odors, concentration-specific trajectories of the 1:1 mixture form odor-specific manifold. Nine-trial averages for each condition. (C) Trajectories corresponding to odor-morphing series. From Oct to Cit: 140:0, 140:30, 140:60, 140:80, 140:100, 140:120, 140:140, 120:140, 100:140, 80:140, 60:140, 30:140, 0:140. Trajectories change smoothly, with greatest changes away from pure- odor.

D-H. Multi-component-mixture trajectories (dataset different from that in A-C: 175 other PNs, stimulated with 44 different odor conditions, see Methods). Four and a half seconds are represented, beginning at odor onset; odor pulses: 500 ms long; 50-ms bins, each averaged over three 2-trial averages. (D) Trajectories in 3-LLE space for the 8 single-odor components. Inset: zoom out of 8 single-odor trajectories together with the 8-mixture trajectory (gray) (LLE axes recalculated). Mixture trajectory loops around those for individual odors. (E) Starting from single odor W, trajectories increasingly deviate as components added (W→WX→WXY→WXYZ→AWXYZ). (F) Mixtures form ordered trajectory clusters: family of {W,X,Y,Z} (W, X, Y, Z, WX, WY, WZ, XY, XZ, YZ, WXY, WYZ, WXYZ) well separated from family of {A,B,C,D} (A, B, C, D, AB, AC, AD, BC, ABC, ACD, ABCD). (G) Trajectories to partly overlapping 4-mixtures. (H) Four D-containing trajectories (D, AD, ACD, ABCD) plotted together with four Z-containing trajectories (Z, WZ, WYZ, DWYZ). DWYZ trajectory (cyan) follows WYZ trajectory for the most part but deviates towards the D-series transiently. Hence, DWYZ can be classified as related to Z or D, depending on time within response (see text).

I. Minimum correlation distances (dmin) between two trajectories as functions of number of components in the mixture (correlation distances minimize contributions of firing rate differences). Each bin of a trajectory (2-trial average) is compared with bins of the other at times t±2bins. Correlation distances in space defined by the 40 first principal components (~70% of variance). Details in text. When comparing distances between single odors and mixtures, upper bound is given by distances between different single odors (red, n=1), because this distribution indicates the separation between non- overlapping stimuli.

2.1.2 Representation of mixtures of increasing complexity by PNs

We next examined PN trajectories for mixtures of increasing number of components. Eight molecules were chosen to be chemically distinct and their concentrations adjusted to evoke minimal, reliable and comparable electro-antennograms, compensating for differences in vapor pressure or receptor activation and ensuring operation away from saturation. The trajectories corresponding to these eight stimuli are shown in Fig. 2.1D.

Consistent with the odors’ distinct chemical composition, these trajectories did not cluster, indicating large differences between the evoked PN response patterns.

We first examine the effect of adding 1<n<7 components to a single odor, W (Fig. 2.1E). The mixture trajectories always deviated from that for W and from each other. For n>3, however, subsequent component addition led to decreasing changes in the population trajectory. This is consistent with the fact that the fractional change to the stimulus decreased with each single component addition. This observation was repeated with the other odors and quantified by analysis in the full PN space (not shown).

Second, we observed that, while mixture representations deviated from those of their components, they still formed clusters of trajectories, well segregated from those corresponding to non-overlapping mixtures. In Fig. 2.1F, sets of all single- and mixed-odor trajectories for odor groups

{W,X,Y,Z} and {A,B,C,_,D} are plotted, revealing two non-overlapping manifolds. This suggests that PN population patterns retain information about components in mixtures, and that PN trajectories do not spread randomly in representation space.

Third, we examined the trajectories corresponding to partly overlapping odors with equivalent strengths (same numbers of components). In this example (Fig. 2.1G) we plot the trajectories of six mixtures. Three pairs had an overlap of 3 out of 4 components (BCWX &

BDWX; ABCD & ABCX; WXYZ & DWYZ) and these pairs clearly clustered together. The other combinations overlapped by two (e.g. BCWX vs. ABCD;

BCWX vs. WXYZ) and were roughly equidistant from one another. This again suggests an ordered occupancy (qualitatively at least) of PN coding space, where distances between population representations decrease as composition overlap increases. Note, however, that overlaps between mixtures representations—considered until now as averages—often changed over the course of a trajectory. Figure 2.1H, for example, plots the trajectories for two groups of odors that were distinct (ABCD vs. WYZ), until component D was added to WYZ. The addition of D caused a new kink in the DWYZ trajectory, bringing it closer to the D family during a short segment of the response. Conversely, two highly overlapping mixtures (overlap of 4 out of 5 components: ADWYZ and AWXYZ) could be represented by PN trajectories that remained nearly identical for a segment of the response,

and then split apart over a later epoch (Fig. S2.8). These results showed that a fair metric of the similarity between two mixture representations should be based not on the totality of their corresponding trajectories, but on piecewise measurements, and on the closest encounter between them. We thus measured the minimum correlation distances between every single-component odor and all other odors (other singles, mixtures of 2, 3, etc.). Using correlation distance (as opposed to Euclidean) has the advantage of focusing on differences in PN population vectors and discounting effects attributed to changes in firing rate (such as concentration). This minimum-distance plot (Fig. 2.1I) was calculated in three ways: between trials (black), to measure the variance of individual population representations; between the representations of each single component and those of all the mixtures containing it (blue); between the representation of each single component and those of all the mixtures excluding it (red). The blue and red curves (and corresponding distributions) were significantly different (Wilcoxon Rank Sum Test, p < 0.01) only for n=1, 2 or 3. Thus, the representations of a monomolecular odor and of mixtures of n>3 components are equally distant (on average over odors, and at the times corresponding to minimum distances) whether the mixture contains that component of not. In conclusion, while PN-representation space clearly shows order from mixture coding, extraction of component composition, based on overlaps between PN population vectors appears difficult if not impossible with mixtures of n>3 components.

Figure 2.2 KCs segment components out of odor mixtures, but PNs do not.

A. Spike rasters of a representative PN to single and mixed odors (see Methods for 44 stimuli, 7 trials, 500-ms stimulus at shaded area, 2.5 s shown). Numbers of components organized by column, conditions arranged so that overlapping mixtures next to each other wherever possible. Increased inhibition often observed for mixtures

5 4 3 2

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with increasing size; responses to mixtures difficult to predict from responses to components (see Fig. S9).

B-C. Spike rasters of six representative KCs (see Figs. S11-14 for more examples). (B) D-segmenting KC, with weak late response to unrelated mixtures Y, WZ, YZ. Same scale as in A. (C) Other representative KCs, showing segmentation of different odors (in order of KCs: W, Y, X, C and W). KCs 5 and 6 recorded simultaneously; both responded to mixtures containing both C and W (e.g., BCWX), but at different times. Only 1 s shown, centered on KC response times; t scale as in B.

D. Conditional probability of response to mixtures, given that cell responds to components (see text and Method). Blue: “in-class”. Black: “out-class”. Lines: “inclusive”;

dashed: “exclusive”. Averaged across all responding cell-odor class pairs. Shaded region: 30-70% distribution. Separation between in-class and out-class much greater for KCs than PNs.

E. ROC evaluation of component selectivity by PNs and KCs. True and false positive rates (TP, FP) determined by sliding response threshold; response based on spike counts within 1 s window summed over 7 trials. Red diagonal: chance performance. Blue lines:

results for each responding cell-odor class pair (see Methods for class partitions).

F. Distribution of area-under-curve (AUC) values for KC-odor class pairs significantly shifted to the right of PN-odor class pairs (p<3.10^-13, Wilcoxon rank sum test). Arrows indicate means: 0.73 (KCs; SD=0.16); 0.57 (PNs; SD=0.18).

2.1.3 Kenyon cell responses to mixtures

Because Kenyon cells are the direct targets of PNs in the mushroom bodies, because mushroom bodies are a site for associative memory (48, 80) and because KC output synapses are plastic (70), KCs are the likely repository of olfactory memories. It is therefore important to determine the stimulus features that they extract from PNs. For comparison, we show first the responses of one representative PN to our 44 stimuli. As is typical of PNs

(53), this neuron responded to about half of the stimuli with a variety of discharge patterns (Fig. 2.2A, see also Fig. S2.10). By contrast, KCs responded very rarely to single odors, but when they did, did so with very high specificity (Figs. 2.2B-C). Surprisingly, KCs that responded to a component also often responded to many—if not all—of the mixtures containing it. KC 1 (Fig. 2.2B), for example, fired in response to odor D, and responded to all mixtures containing D (though not necessarily at the same times and for the same durations). The same can be seen with KCs 2 and 6 for odor W (Fig. 2C). KCs 5 and 6 were recorded simultaneously, and each responded to a different molecule. We found KCs specific to all 8 single odors. (Our pre-experiment search for KCs always focused on these 8 odors, but on them only, see Methods; we also found, by chance and thus rarely, a few KCs specific for binary mixtures; Fig. S2.13). Thus the ability to detect components in a mixture appears to occur first with KCs.

We next analyzed the difference between PN and KC responses using two metrics. In the first, we measured conditional probabilities of response to mixtures, given that a neuron responded to a component (see Methods for definition of response). If a neuron responded to component c, we measured the fraction of c-containing mixtures that it responded to (blue curves). This was repeated for all component-cell combinations with PNs and KCs (Fig. 2.2D). With KCs, this measurements were performed in two ways: an “inclusive” computation contained all cells responding to at least

one component (continuous lines); an “exclusive” computation contained KCs that responded to only one component (stippled line); the later measure is more informative since it excludes the potential contribution of components other than that tested on responses to mixtures. This exclusive computation was not possible with PNs for they always responded to many components. Our second approach was a receiver-operator-characteristics (ROC) analysis (81), measuring a neuron’s ability to separate stimuli into “containing-x” and “not-containing-x” sets, as response threshold is varied. On a true-positive (TP) vs. false-positive (FP) plot, selective neurons are identified by ROC curves located in the upper-left quadrant (Fig. 2.2E). Unselective ones run along the diagonal. The area under the curve (AUC) thus measures selectivity (near 1 for high, near 0.5 for low) (Fig. 2.2F). Both approaches indicated that KCs are significantly better than PNs at component segmentation. ROC analysis proved that this is not explained simply by high KC firing thresholds. Hence, in addition to being highly selective and thus, rare responders, KCs behave as odor segmenters, extracting component information from PN population vectors.

2.1.4 PN and KC population statistics

We quantified population PN and KC activity as a function of n number of odor components in the mixture (Fig. S2.17A). Mean baseline PN firing rate calculated was ~2.5 Hz. For single components, peak firing reached ~ 3 Hz,

around odor offset. Peak instantaneous firing (and total spikes) remained approximately the same as a function n, interestingly, peak firing rate increased for the higher concentration of single components (~3.8 Hz), while mixtures of comparable concentration resulted in a lower firing rate (~2.8 Hz for 4-mixtures, Fig. S2.17A). A closer examination of the response profiles of firing rates reveals that the onset of firing is earlier for mixtures than for components, and this difference cannot be accounted for by concentration alone, e.g., compare peak and onset of 3- mixtures to 4x 1- components. Next, we examined the percentage of silent PNs as a function of time and n components. A cell was defined as silent if it fired no spikes in 100 ms time bins (across 7 trials) to allow for a more conservative measure of silence. The percentage of silent PNs clearly increases as a function of n components (Fig. S2.17B). This reflect increased inhibition by local neurons (LNs) onto PNs. When many components are mixed, this inhibition is greater for mixtures than for components of comparable concentrations. Together, these results suggest a gain control mechanism of mixtures mediated by the PN-LN network that regulates the output of the PNs. Next, we examined the firing rate of the KC population as a function of n (Fig. S2.17A), unlike PNs, instantaneous KC firing increases as a function of n, for ~0.3 Hz for single components to ~0.9 Hz for 8-mixtures. In addition, we observe that unlike PNs, where many cells become inhibited during odor response, most KCs by comparison are silent at rest, and a very small percentage of them become active during response. This small, but

still significant increase in KC firing as a function of n must be attributed to not greater number of PN spikes, but greater synchrony of PN inputs.

An important property of neural codes is the activity ratio, the fraction of active neurons at any one time (82). At one end of the spectrum are local codes, where each stimulus is represented by a single active cell. At the other extreme are dense distributed codes, where each stimulus is represented on average by about half of the cells, e.g., the ASCII code.

Codes with low activity ratios are known as sparse codes, where each stimulus is represented by much a smaller neuronal population (but not 1 cell), the members of which respond in an explicit manner to specific features. The activity ratio has implications for coding capacity, memory recall, generalization, fault tolerance and speed and rules of learning (see Ch 3). Here, we compared the activity ratio between PNs and KCs (Fig. S2.17C).

We measured the responsiveness of cells in short time bins of 50 ms. A cell was defined as responding if it spiked at least once in 4 of 7 trials, and was at least 1.5 SDs above the baseline firing (see Methods). At rest, less than 0.4% of all PNs are responding by this metric, however, with odor onset, the percentage of responsive PNs immediately rose to ~8% for single components, ~13% for higher concentrations of single components, and

~11% for multi-component mixtures. Because the identities of responding PNs change from time bin to time bin, over a 3 s period, ~36-55% of all PNs

responded in at least one time bin (this percentage increased as a function of n). In comparison, there were no responding KCs at baseline, and only a very small subset of them responded with odor onset, ~0.5-1% in any one time bin, and a maximum of ~5% in a 3 s period (to 8- mixture).

These KC response probabilities are qualitatively a 10-, 20- fold over- estimation, because there was a selective bias for single components in the KC recordings (see Methods). These results confirm that PN responses are dense and distributed with a mechanism for gain control of PN outputs. In contrast, KC responses are sparse and rarely respond (this issue is revisited in Ch 3). Interestingly, in a recent modeling study (83), it was shown that optimal discrimination performance is associated with a narrow range of values for sparseness centered at ~1%, matching our KC responsiveness.

Figure 2.3 KCs segment components out of odor mixtures, but PNs do not.

D. Conditional probability of response to mixtures, given that cell responds to components (see text and Method). Blue: “in-class”. Black: “out-class”. Lines: “inclusive”;

dashed: “exclusive”. Averaged across all responding cell-odor class pairs. Shaded region: 30-70% distribution. Separation between in-class and out-class much greater for KCs than PNs.

results for each responding cell-odor class pair (see Methods for class partitions).

Dalam dokumen Neural Encoding of Mixtures and Stimulus Generation in the Insect Brain (Halaman 30-148)